the question is in the more information column

Question

the digits 1, 2, 3, 4, 5, and 6 are randomly arranged to form a three digit number. Digits are not repeated. Find the probability that the number is even and greater than 600

Answer 1

123	124	125	126	134	135	136	145	146	156	234	235
236	245	246	256	345	346	356	456	132	142	152	162
143	153	163	154	164	165	243	253	263	254	264	265
354	364	365	465	213	214	215	216	314	315	316	415
416	516	324	325	326	425	426	526	435	436	536	546
231	241	251	261	341	351	361	451	461	561	342	352
362	452	462	562	453	463	563	564	312	412	512	612
413	513	613	514	614	615	423	523	623	524	624	625
534	634	635	645	321	421	521	621	431	531	631	541
641	651	432	532	632	542	642	652	543	643	653	654

The table shows all possible 3-digit permutations of the digits 1-6. The highlighted ones are even and above 600.

For a 3-digit number to be above 600, the first digit must be a 6. That leaves digits 1-5 to occupy the remaining two digits. There are 20 permutations of the digits 1-5:

12 13 14 15 23 24 25 34 35 45 21 31 41 51 32 42 52 43 53 54 and the 8 highlighted ones are even. Therefore, there are 8 3-digit numbers containing 1-6 which are also over 600. This is confirmed by the table.